Abstract: An ex post perfect public equilibrium (EPPPE) is a PPE that is robust to the possibility that players might observe unmodeled, payoff-irrelevant signals that are correlated with each others’ contemporaneous private information. However, robustness comes at a cost to the players: in many games, efficient payoffs in the corresponding static mechanism design problem cannot be supported as average payoffs in an EPPPE, even when players are patient. In two-player repeated allocation games, an optimal EPPPE never employs a (static) efficient outcome function in any stage game. Instead, the players always prefer to give up some static efficiency by sometimes allocating to the player with the lower valuation. Under independent valuations, optimal equilibria are often stationary, but when valuations are globally interdependent, optimal equilibria are never stationary. Applied to the problem of collusion with hidden costs, these results yield new insights into the phenomenon of price wars in collusive equilibria.

Note: I recently learned of an error in this paper. I am working on figuring out how to correct it, and will post an updated version once I've corrected it. In the meantime, please do not cite older working versions of the paper.

Abstract: We analyze the extent to which efficient trade is possible in an ongoing relationship between impatient agents with hidden valuations (i.i.d. over time), restricting attention to equilibria that satisfy ex post incentive constraints in each period. With ex ante budget balance, efficient trade can be supported in each period if the discount factor is at least one half. In contrast, when the budget must balance ex post, efficiency is not attainable, and furthermore for a wide range of probability distributions over their valuations, the traders can do no better than employing a posted price mechanism in each period. Between these extremes, we consider a "bank" that allows the traders to accumulate budget imbalances over time, but only within a bounded range. We construct non-stationary equilibria that allow traders to receive payoffs that approach efficiency as their discount factor approaches one, while the bank earns exactly zero expected profits. For some probability distributions there exist equilibria that yield exactly efficient payoffs for the players and zero profits for the bank, but such equilibria require high discount factors.

Abstract: This paper proposes a theoretical framework for studying the invention of new products when demand is uncertain. In this framework, under general conditions, the threat of ex post entry by a competitor can deter invention ex ante. Asymmetric market power in the ex post market exacerbates the problem. The implications of these general results are examined in a series of examples that represent important markets in the computer industry. The first is a model that shows how an operating system monopolist, by its mere presence, can deter the invention of complements, to its own detriment as well as that of society. The implications of policies such as patent protection, price regulation, and mandatory divestiture are considered. Three additional examples consider the ability of a monopolist in one market to commit to bundling an unrelated product, a pair of horizontally differentiated firms that can add a new feature to their products, and a platform leader that can be challenged in its base market by the supplier of a complementary product.

Abstract: We present four stylized facts about the Dot Com Era: (1) there was a widespread belief in a “Get Big Fast” business strategy; (2) the increase and decrease in public and private equity investment was most prominent in the internet and information technology sectors; (3) the survival rate of dot com firms is on par or higher than other emerging industries; and (4) firm survival is independent of private equity funding. To connect these findings we offer a herding model that accommodates a divergence between the information and incentives of venture capitalists and their investors. A Get Big Fast belief cascade may have led to overly focused investment in too few internet startups and, as a result, too little entry.